Orientations of faults determined by premonitory shear zones

Abstract

The postulate of premonitory shear zones that the orientations of many faults are controlled by previously formed shear zones is a combination of theoretical analysis and the concept that faulting is the result of a group of hereditary processes. The hereditary nature of faulting processes is evinced by detailed observations of faulting in several, quite different materials in which the faults are end products of irreversible, localized deformation sequences such as pressure solution, particle rearrangement, layer reorientation, plastic flow or grain fracturing. The localized deformation is concentrated within shear zones that premonish the formation of faults. Thus, the problem of determining the orientations of faults becomes one of determining the preferred orientations of shear zones, which is the focus of the postulate of premonitory shear zones. The postulate is based on one definition and two assumptions: by definition, deformation becomes localized within a shear zone (the reason need not be specified); by assumption, the virtual shearing and dilation within the shear zone are coupled and the orientation that develops corresponds to the preferred orientation. The preferred orientation of the shear zone is defined as that which satisfies the mechanical and kinematical boundary conditions and maximizes, in some sense, the virtual work accomplished by the shearing and dilation. With the exception of coupling of the shearing and dilation through a coefficient of dilation, the analysis is only implicitly dependent on rheology; the only rheological requirement is that the properties allow localization. Although the postulate is based on very simple assumptions, and so its predictions are necessarily simple, it has a power that belies its simplicity. The preferred orientations of premonitory shear zones are consistent with orientations of shear zones and faults in laboratory specimens of Chelmsford granite. The coefficient of dilatancy in granite specimens about to fault is known to be positive. According to the postulate, the shear zones should be oriented at angles less than 45° to the compression direction, and it is well known that faults in rock specimens have such orientations. The postulate also predicts the strikingly different orientations of kink bands in foliated materials. Unlike faults in granite specimens, kink bands and the faults that form along them are commonly oriented at angles greater than 45° to the maximum compression. Analysis of kink-band formation indicates that the coefficient of dilatancy is typically negative if the contact strength between layers is frictional, and the postulate affirms that the negative dilatancy will result in the observed orientations. Associations of faults with well-defined shear zones consisting of numerous deformation bands in the Entrada Sandstone in Utah's San Rafael Desert illustrate clearly the control that premonitory shear zones have over the orientations of faults in these rocks. The orientations of conjugate shear zones, both in normal and strike-slip systems, indicate that the angle of dilatancy of the sandstone was about 60°, indicating that the dilatancy was positive at the time the orientations of the shear zones were determined, in spite of microscopic evidence that the volume decreased at some time during the formation of the shear zones. The faults that Gerhard Oertel produced in claycake experiments are amazing, but their orientations can be understood in terms of the postulate of premonitory shear zones: These experiments emphasize, perhaps more strongly than any of the other examples we have considered, the importance of understanding the mechanisms of deformation in the material under study. In compression experiments, the angle between the maximum compression and the faults is a highly obtuse angle of 83° whereas, in extension experiments, the angle is a highly acute angle of 7°! The postulate indicates that, in compression experiments, the clay had a very large, negative angle of dilatancy, −76°. It also indicates that, in the extension experiments, the angle of dilatancy was the same, but opposite in sign (+ 76°). The different senses of dilatancy are consistent with the behavior of clayey soils in geotechnical experiments; in a shear test, clay-water mixtures consolidate if they are underconsolidated and dilate if they are overconsolidated relative to the normal stress. Thus, the postulate explains the peculiar orientations of the faults in Oertel's claycake experiments in terms of the peculiar dilatancies of clay-water mixtures. Thus, the postulate provides a much needed, albeit tentative, explanation for the orientations of shear zones and the faults that ultimately form along them. It provides a viable replacement for Anderson's theory of fault orientations and provides further motivation for investigating the mechanics and chemistry of localization of deformation, which is so common in geology, resulting in veins, stylolites, slaty and crenulation cleavages, kink folds, and a wide variety of faults.